Overallforce equilibrium in ydirection gives: (6) (7) Overallmoment equilibrium in the ydirection gives: Equations for directional factors of safety Fx, Fy, Fmx, Fmy can be. The equilibrium equation has been separated into three components corresponding to the x, y, and z axes for both the forces and. Overallforce equilibrium in xdirection gives: (4) Overallmoment equilibrium in the xdirection gives: (5) where RX, RY, and RZ are lever arms to the moment point. The FBD shows the object and all the forces acting on it, and defines the symbols we will use. For the expanded equation, each coefficient of the i, j, and k unit vectors must equal zero for static equilibrium. It is important to follow the right-hand rule when defining the coordinate system.ĭraw a free-body diagram. Normally this will be a system with the origin at the particle or directly below the particle, a horizontal \(x\) axis, a vertical \(y\) axis, and the \(z\) axis coming out of the page and towards you. The particle will be the object or point where the lines of action of all the forces intersect.Įstablish a coordinate system. The overall procedure is presented here and then each of the new steps is explained in more detail. When working in three dimensions there are three important angles, but the general procedure is the same. The major differences are that you must be very careful about the orientation and direction of each axis of the coordinate frame and the angles each vector makes with each axis. The general procedure for solving equilibrium of a particle (or concurrent force) problems in three dimensions is essentially the same as for two dimensions using the components method.
So if you know two direction cosine angles you can find the third from this relationship.
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